Quantifying Inefficiency

We axiomatically define a cardinal social inefficiency function, which, given a set of alternatives and individuals’ vNM preferences over the alternatives, assigns a unique number – the social inefficiency – to each alternative. These numbers – and not only their order – are uniquely defined by our axioms despite no exogenously given interpersonal comparison, outside option, or disagreement point. We interpret these numbers as per-capita losses in endogenously normalized utility. We apply our social inefficiency function to a setting in which interpersonal comparison is notoriously hard to justify – object allocation without money – leveraging techniques from computer science to prove an approximate-efficiency result for the Random Serial Dictatorship mechanism.